Problem: $J$ $K$ $L$ If: $ JK = 4x + 4$, $ JL = 31$, and $ KL = 2x + 9$, Find $KL$.
From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {4x + 4} + {2x + 9} = {31}$ Combine like terms: $ 6x + 13 = {31}$ Subtract $13$ from both sides: $ 6x = 18$ Divide both sides by $6$ to find $x$ $ x = 3$ Substitute $3$ for $x$ in the expression that was given for $KL$ $ KL = 2({3}) + 9$ Simplify: $ {KL = 6 + 9}$ Simplify to find ${KL}$ : $ {KL = 15}$